Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
On Software Parallel Implementation of Cryptographic Pairings
Selected Areas in Cryptography
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Montgomery multiplication on the cell
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
High-performance modular multiplication on the cell processor
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
On the correct use of the negation map in the Pollard rho method
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
High-speed high-security signatures
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
International Journal of Applied Cryptography
International Journal of Applied Cryptography
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Elligator: elliptic-curve points indistinguishable from uniform random strings
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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This paper is the first to investigate the power of the Cell Broadband Engine for state-of-the-art public-key cryptography. We present a high-speed implementation of elliptic-curve Diffie-Hellman (ECDH) key exchange for this processor, which needs 697080 cycles on one Synergistic Processor Unit for a scalar multiplication on a 255-bit elliptic curve, including the costs for key verification and key compression. This cycle count is independent of inputs therefore protecting against timing attacks. This speed relies on a new representation of elements of the underlying finite field suited for the unconventional instruction set of this architecture. Furthermore we demonstrate that an implementation based on the multi-precision integer arithmetic functions provided by IBM's multi-precision math (MPM) library would take at least 2227040 cycles. Comparison with implementations of the same function for other architectures shows that the Cell Broadband Engine is competitive in terms of cost-performance ratio to other recent processors such as the Intel Core 2 for public-key cryptography. Specifically, the state-of-the-art Galbraith-Lin-Scott ECDH software performs 27370 scalar multiplications per second using all four cores of a 2.5GHz Intel Core 2 Quad Q9300 inside a $296 computer, while the new software reported in this paper performs 27474 scalar multiplications per second on a Playstation 3 that costs just $221. Both of these speed reports are for high-security 256-bit elliptic-curve cryptography.